Results 1 to 10 of about 409,288 (165)
Γ-convergence of free-discontinuity problems [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2019 We study the Γ-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in
Filippo Cagnetti +3 more
openaire +7 more sources
Stochastic Homogenisation of Free-Discontinuity Problems [PDF]
Archive for Rational Mechanics and Analysis, 2019 23 ...
Cagnetti, F. +3 more
openaire +6 more sources
Iterative Thresholding Meets Free-Discontinuity Problems [PDF]
Foundations of Computational Mathematics, 2010 Free-discontinuity problems describe situations where the solution of interest is defined by a function and a lower dimensional set consisting of the discontinuities of the function. Hence, the derivative of the solution is assumed to be a `small' function almost everywhere except on sets where it concentrates as a singular measure.
Fornasier, Massimo, Ward, Rachel
openaire +5 more sources
Manifold-constrained free discontinuity problems and Sobolev approximation [PDF]
Nonlinear Analysis, 2023 We study the regularity of local minimisers of a prototypical free-discontinuity problem involving both a manifold-valued constraint on the maps (which are defined on a bounded domain $Ω\subset \R^2$) and a variable-exponent growth in the energy functional.
Dipasquale, Federico Luigi +1 more
openaire +4 more sources
Degenerate Free Discontinuity Problems and Spectral Inequalities in Quantitative Form [PDF]
Archive for Rational Mechanics and Analysis, 2021 We introduce a new geometric-analytic functional that we analyse in the context of free discontinuity problems. Its main feature is that the geometric term (the length of the jump set) appears with negative sign. This is motivated by searching quantitative inequalities for best constants of Sobolev-Poincaré inequalities with trace terms in $\mathbb{R ...
Bucur D., Giacomini A., Nahon M.
openaire +5 more sources
Strong Existence for Free-Discontinuity Problems with Nonstandard Growth [PDF]
SIAM Journal on Mathematical AnalysisarXiv admin note: text overlap with arXiv:2303 ...
Leone, Chiara +3 more
openaire +5 more sources
Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems [PDF]
2017 IEEE International Conference on Computer Vision (ICCV), 2017 In this work we show how sublabel-accurate multilabeling approaches can be derived by approximating a classical label-continuous convex relaxation of nonconvex free-discontinuity problems. This insight allows to extend these sublabel-accurate approaches from total variation to general convex and nonconvex regularizations.
Möllenhoff, Thomas, Cremers, Daniel
openaire +4 more sources
Multiphase free discontinuity problems: Monotonicity formula and regularity results
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2021 The purpose of this paper is to analyze regularity properties of local solutions to free discontinuity problems characterized by the presence of multiple phases. The key feature of the problem is related to the way in which two neighboring phases interact: the contact is penalized at jump points, while no cost is assigned to no-jump interfaces which ...
Bucur, Dorin +2 more
openaire +7 more sources
Strong Existence for Free Discontinuity Problems in Linear Elasticity
SIAM Journal on Mathematical AnalysisIn this note we show Ahlfors-regularity for a large class of quasiminimizers of the Griffith functional. This allows us to prove that, for a range of free discontinuity problems in linear elasticity with anisotropic, cohesive, or heterogeneous behavior, minimizers have an essentially closed jump set and are thus strong minimizers.
Manuel Friedrich +2 more
openaire +3 more sources
Relaxation results for some free discontinuity problems.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1995 In many problems of Mathematical Physics one is concerned with minimum problems for functions defined on function spaces allowing discontinuities. When the discontinuity set is not a priori given the problem is called with ``free discontinuity'' and it would be helpful, for the existence theory and for the study of minimizing sequences, the knowledge ...
Braides, Andrea +2 more
openaire +2 more sources